Searching sparse solutions from overcomplete models: selected applications
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Proceedings |
| Conference | Proceedings of the Summer School DATASTAT'2006 |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | approximation; atomic decomposition; sparsity; smoothing; time series; forecasting; ROC/ODC curve. |
| Description | When solving real problems there is often missing a reliable theory behind them. In such situations the ideas about a choice of an appropriate model are very vague and produce models where it is hard to balance the requirement on sufficient regularity of the model (as few parameters as possible to guarantee numerical stability) and its sufficient precision which forces the analyst to increase the number of model components typically leading to overparametrization (overcompleteness) accompanied with non-uniqueness and numerical instability of solutions. The technique based on the Basis Pursuit Algorithm originally suggested by Chen et al [SIAM Review 43 (2001), No. 1] for the processing of digital signals allows one to find sparse stable solutions from such models. In this paper its performance and flexibility is demonstrated by the solution of four problems coming from completely diverse application fields: smoothing (denoising), time series forecasting, analysis of air pollution by suspended particulate matter and ROC/ODC curve estimation. |
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